Modern methods of treatment have led to a major improvement in the survival rate of children with Wilms' tumor. In recent years, surgery, radiation therapy and chemotherapy cures up to 80 percent of patients. At the same time it is recognized that all treatment forms have their risks and complications. The efforts of many researchers in recent years have been directed toward a greater understanding of the disease and to refining methods of management so as to achieve maximum survival with the least morbidity. The national yearly incidence of Wilms' tumor, estimated to be 500 is too low for it to be feasible for even the largest pediatric institutions to conduct purely intramural comparative clinical trials. Therefore, groups of investigators in institutions with a common interest in the Wilms' tumor problem agreed to combine their efforts in a single investigation. Many institutions and investigators - both members of cooperative groups and those hitherto unaffiliated in such endeavors - have joined in this endeavor. The primary objectives of the study are to answer two specific questions: (1) is post-operative radiotherapy necessary for the treatment of patients with localized tumors that are completely removed? (2) Which of the two chemotherapeutic agents, Actinomycin D and Vincristine, both known to be effective against Wilms' tumor, gives the better result and can this result be improved by their combined use? Secondary objectives of the study are to obtain a better understanding of the neoplasm by grouping the patients and determining the response of the different groups, and to assess if different histologic types can be correlated with prognosis.